The correct option is **C. Force**. ### Detailed Explanation 1. **Understanding Derived and Base Quantities**: - In the International System of Units (SI), quantities are classified into two categories: base quantities and derived quantities. - **Base quantities** are fundamental physical quantities that are defined independently. They include: - Length (meter, m) - Mass (kilogram, kg) - Time (second, s) - **Derived quantities** are those that are derived from the base quantities through mathematical relationships. They are not defined independently but are calculated using base quantities. 2. **Identifying the Options**: - **A. Length**: This is a base quantity. It is measured in meters (m) and does not depend on other quantities. - **B. Mass**: This is also a base quantity. It is measured in kilograms (kg) and is fundamental to the measurement of matter. - **C. Force**: This is a derived quantity. It is defined as the product of mass and acceleration (Newton's second law of motion). The unit of force is the Newton (N), which can be expressed in terms of base units as: \[ 1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2 \] Here, force is derived from the base quantities of mass (kg) and length (m) and time (s). - **D. Time**: This is a base quantity. It is measured in seconds (s) and is fundamental to the measurement of duration. 3. **Why Other Options Are Incorrect**: - **A. Length**: Incorrect because it is a base quantity, not derived. - **B. Mass**: Incorrect because it is a base quantity, not derived. - **D. Time**: Incorrect because it is a base quantity, not derived. ### Common Pitfalls - Students often confuse derived quantities with base quantities, especially when they involve multiple base quantities. Remember that derived quantities are formed from combinations of base quantities. - It’s important to memorize the base quantities in the SI system to easily identify derived quantities. ### Summary - **Derived quantities** are formed from base quantities through mathematical relationships. - **Force** is a derived quantity, calculated as mass times acceleration. - **Length, mass, and time** are all base quantities in the SI system. - Understanding the distinction between base and derived quantities is crucial for mastering physics concepts. ### Revision Summary - Base quantities: Length, Mass, Time (independent). - Derived quantity: Force (dependent on base quantities). - Force is calculated using the formula \( F = m \cdot a \). - Remember the units: 1 N = 1 kg·m/s² for force.